The arithmetic sequence $(a_i)$ is defined by the formula: $a_1 = -2$ $a_i = a_{i-1} - 5$ What is $a_{20}$, the twentieth term in the sequence?
Solution: From the given formula, we can see that the first term of the sequence is $-2$ and the common difference is $-5$ To find the twentieth term, we can rewrite the given recurrence as an explicit formula. The general form for an arithmetic sequence is $a_i = a_1 + d(i - 1)$ . In this case, we have $a_i = -2 - 5(i - 1)$ To find $a_{20}$ , we can simply substitute $i = 20$ into the our formula. Therefore, the twentieth term is equal to $a_{20} = -2 - 5 (20 - 1) = -97$.